y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...

8. First-Order Equations: Numerical Methods 8.1. Numerical Approximations 2 8.2. Explicit and Implicit Euler Methods 3 8.3. Explicit One-Step Methods Based on Taylor Approximation 4 8.3.1. Explicit Euler Method Revisited 4 8.3.2. Local and Global Errors 4 8.3.3. Higher-Order Taylor-Based Methods (not covered) 5 8.4. Explicit One-Step Methods Based on Quadrature 6 8.4.1. Explicit Euler Method Re...

there are many occasions where the base of a robotic manipulator is attached to a moving platform, such as on a moving ship, terrain or space shuttle. in this paper a dynamic model of a robotic manipulator mounted on a moving base is derived using both newton-euler and lagrange-euler methods. the presented models are simulated for a mitsubishi pa10-6ce robotic manipulator characteristics mounte...

This paper presents a case study of numerical simulations in an easy-to-use matrix computation framework named Simple Interface for Library Collections (SILC), which allows users to use various matrix computation libraries in an environmentand language-independent manner. As a practical example of numerical simulations in SILC, we selected cloth simulation based on a mass-spring model and the i...

We prove necessary optimality conditions of Euler–Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kind of variational problems were considered by Euler himself and ha...

Abstract. We investigate the strong convergence rate of both Runge–Kutta methods and simplified step-N Euler schemes for stochastic differential equations driven by multi-dimensional fractional Brownian motions with H ∈ ( 2 , 1). These two classes of numerical schemes are implementable in the sense that the required information from the driving noises are only their increments. We prove the sol...

Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-steppingmethod to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods ...

An explicit time-stepping method is developed for adaptive solution of time-dependent partial differential equations with first order derivatives. The space is partitioned into blocks and the grid is refined and coarsened in these blocks. The equations are integrated in time by a Runge-KuttaFehlberg method. The local errors in space and time are estimated and the time and space steps are determ...